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HYMS phase II H&S > Statistics, definitions and calculations > Flashcards

Statistics, definitions and calculations Flashcards

1
Q

How do you work out sensitivity?

A

Number of true positives/ all those with disease.

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2
Q

How do you work out specificity?

A

Number of true negatives/ all those without disease.

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3
Q

How do you calculate the negative predictive value?

A

Number of true negatives/ all those that test negative.

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4
Q

How do you calculate positive predictive value?

A

Number of true positives/ all those that test positive.

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5
Q

How do you calculate the likelihood ratio for a positive result?

A

The chance that a test is positive if a patient has the disease/ the chance that the test is positive if the patient is well.

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6
Q

How do you calculate the likelihood ratio for a negative result?

A

The chance that a test is negative if a patient has the disease/ the chance that the test is negative if the patient is well.

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7
Q

The larger the positive likelihood ratio….

A

… the greater the chance that you have the disease is your test is positive.

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8
Q

The smaller the negative likelihood ratio…

A

… the lesser the chance that you have the disease if your result is negative.

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9
Q

How do you calculate the chances of having a disease after a test?

A

The chances of having the disease before the test x likelihood ratio.

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10
Q

What is a nomogram?

A

A way of relating the likelihood ratios to the pre and post test probabilities.

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11
Q

What does the vertical line on a forrest plot represent?

A

The line of null effect.

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12
Q

What does the horizontal axis on a forrest plot represent?

A

The statistic that the studies are profiled to show.

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13
Q

Where is the line of null effect placed on a forrest plot?

A

At the value where there is no association between an exposure and outcome or no difference between 2 interventions.

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14
Q

In which cases will the line of null effect be placed at 1?

A

For relative statistics such as an odds ratio or a relative risk as these have a null effect value of 1.

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15
Q

In which cases will the line of null effect be placed at 0?

A

For absolute statistics such as absolute risk, ARR or SMD (standardised mean difference) as the null difference value for these is 0.

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16
Q

What does each horizontal line put onto a forrest plot represent?

A

A separate study which is being analysed.

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17
Q

Each study result being represented on a forrest plot has 2 components to it, what are they?

A

1) A black square box.

2) A horizontal line.

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18
Q

What does each individual black square box represent on a forrest plot?

A

A point estimate of the study result and the size of the study.

The bigger the box, the more participants in the study.

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19
Q

What does each individual horizontal line on a forrest plot represent?

A

The 95% confidence intervals of the study.

Each end of the line represents the boundaries of the confidence intervals.

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20
Q

What does the term ‘95% confidence interval’ mean?

A

The range of values within which you can be 95% certain the true value lies.

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21
Q

What does it mean if the horizontal line of a study crosses the line of null effect?

A

This means that the null value lies within the confidence interval and hence could be the true value.

**Basically, any study which crosses the line of null effect does not illustrate a statistically significant result.

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22
Q

What is a basic rule of thumb linking the size of a study and the horizontal line of the study?

A

Often, the bigger the study, the smaller the horizontal line. This means that it is less likely that those studies will cross the line of null effect because the 95% confidence intervals should have a much smaller range.

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23
Q

What is potentially the most important factor to look at on a forest plot?

A

The diamond at the bottom of the results.

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24
Q

What does the black diamond on a forest plot represent?

A

The point estimate and confidence intervals when you combine and average all of the individual studies together.

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25
Q

1) What do the horizontal points of the diamond represent?

2) What do the vertical points of the diamond represent?

A

1) The 95% confidence intervals of the combined point estimate.
2) The point estimate of the averaged studies.

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26
Q

On a forest plot, what does the column n/N mean which is immediately to the left of the forest plot?

A

n = the number of patients or individuals which had the event/ outcome in that particular group.

N = the total number of people in that group.

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27
Q

What is meant by the term ‘subtotal’ on a forest plot?

A

Tells you the total number of people in the treatment and control groups across all individual studies.

Also shows the average statistic and 95% confidence interval.

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28
Q

In order to assess the consistency of the papers analysed and shown on a forest plot, what statistic is used?

A

I squared.

**The I-squared statistic gives you an idea of the heterogeneity of the studies.

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29
Q

What is the rule of thumb about the I-squared statistic and heterogeneity of papers in a systematic review?

A

You want I-squared to be <50% because anything higher means that the papers could be inconsistent due to a reason other than chance.

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30
Q

If a study shown on a forest plot contains the null value in its 95% confidence interval, what is this likely to mean with regards to the p value?

A

It is most likely to mean that the p value for that study is >0.05 and that the study result is not statistically significant.

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31
Q

What is relative risk?

A

The ratio of the probability of an event occurring in the exposed group versus the non-exposed group OR the probability of an event occurring in a treatment group versus in a placebo group.

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32
Q

What is the calculation for calculating relative risk?

A

(a/a+b)/(c/c+d)

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33
Q

How do you calculate relative risk reduction?

A

(event rate in control group - event rate in treatment group) / event rate in control group.

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34
Q

What is absolute risk reduction?

A

The difference in event rate between control group and treatment group.

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35
Q

How do you calculate absolute risk reduction?

A

Event rate in control group - event rate in treatment group.

**a/(a+b) - c/(c+d)

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36
Q

What is meant by number needed to treat?

A

The number of people you need to treat with a drug in order to prevent one bad thing happening.

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37
Q

How do you calculate number needed to treat?

A

1 / absolute risk reduction.

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38
Q

Name 3 types of data.

A

Interval
Ordinal
Nominal

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39
Q

Describe what is meant by each of the following types of data:

1) Interval
2) Ordinal
3) Nominal

A

1) Quantitative data. Can be discrete (where only certain values are possible; number of falls/ attendance) or continuous (where any value is possible; height/ weight)
2) Qualitative but ordered. There are more than 2 categories which have a logical order (e.g. satisfaction with service).
3) Qualitative multi-nominal data with more than 2 categories that are not ordered (e.g. marital status).

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40
Q

Describe normal distribution.

A

A continuous, symmetrical, uni-modal distribution described by a mathematical equation.

41
Q

What is the point of inflection?

A

The place where 1 standard deviation ends.

42
Q

What is derived data?

A

Data that undergoes conversion or analysis following initial collection.

43
Q

Describe where the mean, mode and median values all lie in a normal distribution curve.

A

Mean, mode and median are all equal and lie at the peak of the curve.

44
Q

In normal distribution, what do you expect to lie within 1 SD of the mean?

A

You expect 68% of observations to lie within this range.

45
Q

In a normal distribution, what do you expect to lie within 2 SDs of the mean?

A

You expect 95% of observations to lie within this range.

46
Q

What is a standard normal distribution?

A

This is a normal distribution with a mean of 0 and a standard deviation of 1.

47
Q

Describe the mean, median and mode in a negative skew of data.

A

Mean < Median < Mode.

48
Q

Describe the mean, median and mode in a positive skew of data.

A

Mode > Median > Mean.

49
Q

Name 3 measures of dispersion.

A

SD
Interquartile range
Range

50
Q

Name 3 measures of location.

A

Mean
Median
Mode

51
Q

What is the difference between null and alternate hypotheses?

A

Null = state that there is no difference or no effect.

Alternate = state that there is a difference or that there is an effect.

52
Q

What does it mean if the probability is:

1) 0?
2) 1?

A

1) Something is certain not to happen.

2) Something is certain to happen.

53
Q

What does a p-value show?

A

The p-value shows the probability that a null hypothesis is true.

54
Q

What is standard deviation?

A

Expresses variation of the data around a mean.

**Shows how spread out the data is in a distribution.

**Used when talking about distributions.

55
Q

What does standard error show?

A

How good an estimate is. It is used to describe the precision in the sample mean.

**Used when talking about estimates found from a sample.

56
Q

1) When should you quote standard error of the mean?

2) When should you quote standard deviation?

A

1) When we want to say how good our estimate of the mean measurement is.
2) When we want to say how widely scattered the measurements are.

57
Q

How do you calculate standard error of the mean?

A

standard deviation / square root of sample size

58
Q

When will the value for the standard error of the mean be smaller?

A

With a larger sample size.

59
Q

How do you calculate the standard error of a proportion?

A

SQUARE ROOT of p x (1 - p) / n

60
Q

What is a confidence interval?

A

A range of values that probably contain the population mean or proportion.

61
Q

What are confidence limits?

A

Values that state the boundaries of the confidence interval.

62
Q

What does it mean to have a 95% confidence interval?

A

That you are 95% certain that the true value for a population lies within this range.

63
Q

How do you calculate a confidence interval?

A

(mean ± z score) x (standard deviation / square root of n)

**this calculation gives you the upper and lower confidence limits.

64
Q

1) What is a z score?

2) What is the z score for a 95% confidence interval?

A

1) A number that corresponds to the percentage of confidence interval you want to calculate.
2) 1.960

65
Q

If a confidence interval does not include the null hypothesis value, what can you deduce?

A

That the difference is significant.

66
Q

If a confidence interval contains the null hypothesis value, what can you deduce?

A

That the difference is not significant.

67
Q

What do hypothesis tests allow us to do?

A

Establish the likelihood that the association we are observing is genuine, or simply due to chance.

68
Q

What happens as a p value becomes smaller?

A

There is an increased likelihood that the null hypothesis will be disproven.

69
Q

What is the conventional threshold for statistical significance?

A

p = 0.05.

70
Q

What does it mean if a p value is <0.05?

A

This means that it IS statistically significant.

**Indicates strong evidence against the null as there is a less than 5% chance that the null is correct.

**Means that the null can be rejected.

71
Q

What does it mean if a p value is >0.05?

A

This means that it IS NOT statistically significant.

72
Q

1) What is a type I error?

2) What is a type II error?

A

1) Incorrect rejection of the null (false positive).

2) Acceptance of a false null (false negative).

73
Q

Define risk.

A

The probability that an event will occur during a specified time.

**number who get the thing or event/ total number of people

74
Q

How do you calculate risk ratio/ relative risk?

A

Risk in exposed group / risk in unexposed group.

75
Q

How do you calculate relative risk?

A

(number with disease in exposed group / total exposed) DIVIDED BY (number with disease in unexposed group / total unexposed).

76
Q

1) What does a risk ratio of 1 imply?
2) What does a risk ratio <1 imply?
3) What does a risk ratio >1 imply?

A

1) No difference in risk between exposed and unexposed.
2) Exposure had a protective influence over outcome.
3) Exposure increased risk outcome.

77
Q

How do you calculate odds?

A

probability that ‘x’ happens / probability that ‘x’ does not happen.

** (p x ‘x’) / 1 - (p x ‘x’)

78
Q

How do you calculate an odds ratio?

A

Odds in exposed group / odds in unexposed group.

79
Q

Define hazard.

A

The risk at any given time of reaching the endpoint outcome in a survival analysis.

80
Q

What do hazard ratios look at?

A

The influence of an exposure on an outcome over time.

81
Q

How do you calculate a hazard ratio?

A

Hazard in exposed group / hazard in unexposed group.

82
Q

Define number needed to treat.

A

The number of patients that would need to receive an intervention in question in order to prevent one adverse event from occurring.

83
Q

How do you calculate number needed to treat?

A

1 / ARR.

**ALWAYS round number needed to treat UP.

84
Q

How do you calculate absolute risk reduction?

A

Event rate in control group - event rate in treatment group.

85
Q

When are the terms sensitivity, specificity and likelihood ratios often used?

A

When referencing the effectiveness of a diagnostic tool.

86
Q

1) Define sensitivity.

2) Define specificity.

A

1) The proportion of those with disease who are correctly identified by a test.
2) The proportion of those without disease who are correctly identified by a test.

87
Q

What is the likelihood ratio for a positive result?

A

The chance of a true positive result versus that of a false positive.

88
Q

What are predictive values influenced by?

A

The prevalence of a disease amongst those in the study.

**LRs are not influenced by the prevalence of disease.

89
Q

How do you calculate sensitivity?

A

Number of true positives / all those with disease.

90
Q

How do you calculate specificity?

A

Number of true negatives / all those without disease.

91
Q

Define positive predictive value.

A

Chance of having the disease if your test is positive.

92
Q

Define negative predictive value.

A

Chance of not having the disease if your test is negative.

93
Q

How do you calculate the positive predictive value?

A

Number of true positives / all those who text positive.

94
Q

How do you calculate the negative predictive value?

A

Number of true negatives / all those who test negative.

95
Q

Describe the relationship between prevalence, NPV and PPV.

A

As prevalence rises, NPV falls and PPV rises.

96
Q

1) The larger the LR+ …

2) The smaller the LR- …

A

1) … the greater chance you have the disease if your test is positive.
2) … the lesser the chance you have the disease if your test is negative.

97
Q

What do tests with a high sensitivity do?

A

Correctly classify a high proportion of people who really have a disease.

98
Q

What do tests with a high specificity do?

A

Correctly classify a high proportion of people who do not have a disease.

HYMS phase II H&S (12 decks)

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